Classification of psychopathology
Traditional taxonomies: categorical diagnostic systems
(e.g., DSM, ICD)
Recent models: dimensional and transdiagnostic approaches
(e.g. Hierarchical Taxonomy of Psychopathology model by Kotov et al., 2017)
How can we uncover latent factors across disorders?
NMF factorizes the full observed data matrix
\(M_{kg} \in \mathbb{R}_{\ge 0}^{K \times G}\),
where each row \(k\) represents an observed feature (e.g., test item)
and each column \(g\) represents an individual.
It decomposes \(M\) into two lower-rank nonnegative matrices:
\(P \in \mathbb{R}_{\ge 0}^{K \times N}\) → loadings of observed variables on \(N\) latent factors
\(E \in \mathbb{R}_{\ge 0}^{N \times G}\) → expression (or weights) of latent factors across individuals
\[ M_{kg} = \sum_{n=1}^{N} P_{kn} E_{ng} \]
Use the NMF on a dataset of ordinal data (Likert scale)
Estimate latent factors
Compare them with those obtained through factor analysis
mostra il codice sul dataset di tommaso
how to make the NMF recognize that items within the same questionnaire have a structure
If the results are encouraging …
Third step: use NMF to find latent factors shared within the same spectrum of symptoms
Fourth step: use causal NMF to find latent factors across different treatment on the same spectrum of symptoms
All materials are available on GitHub at laurasitaunipd/nmf
Kotov, R., Krueger, R. F., Watson, D., Achenbach, T. M., Althoff, R. R., Bagby, R. M., … & Zimmerman, M. (2017). The Hierarchical Taxonomy of Psychopathology (HiTOP): A dimensional alternative to traditional nosologies. Journal of abnormal psychology, 126(4), 454.
Landy, J. M., Basava, N., & Parmigiani, G. (2025). bayesNMF: Fast Bayesian Poisson NMF with Automatically Learned Rank Applied to Mutational Signatures. arXiv preprint arXiv:2502.18674.
Landy, J. M., Zorzetto, D., De Vito, R., & Parmigiani, G. (2025). Causal Inference for Latent Outcomes Learned with Factor Models. arXiv preprint arXiv:2506.20549.
HandZone October 30th, 2025